Multi-unit Auction DesignMulti-unit Auction Design for Salinity Management, Water Auctions and for Salinity Management, Water Auctions and

other NRM Servicesother NRM Services

bybyAtakelty HailuAtakelty Hailu

School of Agricultural and Resource EconomicsSchool of Agricultural and Resource EconomicsUniversity of Western AustraliaUniversity of Western Australia

CAER Workshop Presentation, Sydney, 1 February 2007CAER Workshop Presentation, Sydney, 1 February 2007

OutlineOutline• Three main elements in presentationThree main elements in presentation

• 1) Multi-unit auctions (1) Multi-unit auctions (Based on research done jointly Based on research done jointly with Sophie Thoyer (ENSAM/Lameta) and published as with Sophie Thoyer (ENSAM/Lameta) and published as Multi-unit auction format designMulti-unit auction format design, Journal of Economic , Journal of Economic

Interaction and Coordination, volume 1: 129-146, 2006Interaction and Coordination, volume 1: 129-146, 2006 ))• how multi-unit auctions could improve how multi-unit auctions could improve conservation/water auctionsconservation/water auctions• design of multi-unit auctionsdesign of multi-unit auctions

• what payment rules: pay-as-bid, uniform what payment rules: pay-as-bid, uniform pricing (or Vickrey pricing)pricing (or Vickrey pricing)• report results from computational report results from computational experimentsexperiments

Outline …Outline … 2) MAPPER – a multi-unit auction trial in WA2) MAPPER – a multi-unit auction trial in WA

• organized by Frank D’Emden at DAFWAorganized by Frank D’Emden at DAFWA

3) HydroEcon – an integrated and agent-based 3) HydroEcon – an integrated and agent-based economic-environmental model that we have been economic-environmental model that we have been building at UWA/Salinity CRCbuilding at UWA/Salinity CRC

Auctions for conservationAuctions for conservationAuctions are increasingly used to purchase conservation Auctions are increasingly used to purchase conservation services and, in some cases, to (re)-allocate water user services and, in some cases, to (re)-allocate water user rights:rights:

• Examples:Examples:• US Conservation Reserve Program (CRP), since US Conservation Reserve Program (CRP), since 19851985• BushTender BushTender • MBI Pilot Auctions in Australia (MBI1 and MBI2)MBI Pilot Auctions in Australia (MBI1 and MBI2)• Water buybacks: Purchase of water for Water buybacks: Purchase of water for environmental flows – one sided auctionsenvironmental flows – one sided auctions

Examples: Georgia, Texas, OregonExamples: Georgia, Texas, Oregon

The lumpy bid problemThe lumpy bid problem• Conservation auctions and water auctions are generally Conservation auctions and water auctions are generally single bid auctions (lumpy bids): single bid auctions (lumpy bids):

• a bid consists of a single price-quantity paira bid consists of a single price-quantity pair• example:example:

• will conserve 20 hectares if paid $2000 a will conserve 20 hectares if paid $2000 a yearyear• will forgo 2000 KL if paid $500will forgo 2000 KL if paid $500

• A bidder can submit different bids but they would be A bidder can submit different bids but they would be independent bids/projects (not nested or incremental independent bids/projects (not nested or incremental bids)bids)• Reality: increasing marginal costs of forgoing water, Reality: increasing marginal costs of forgoing water, conservation services, etcconservation services, etc

AN EXAMPLE: BIDDING TO AN EXAMPLE: BIDDING TO SAVE WATERSAVE WATER

Opportunity cost/unit of water saved

Quantity of water saved

1

2

31: water saving practices2: water saving technology3: stop irrigation

The lumpy bid problem …The lumpy bid problem …• Single bid auctions might discourage bidding with Single bid auctions might discourage bidding with large quantities – average cost of delivering service large quantities – average cost of delivering service increases with size of projectincreases with size of project• Losses of potential contracts and misallocation of Losses of potential contracts and misallocation of conservation contracts conservation contracts

• Differences in marginal costs are not exploited wellDifferences in marginal costs are not exploited well• Leads to budgetary and social efficiency lossesLeads to budgetary and social efficiency losses

Farmer 1

Farmer 2MCost$/unit

Q

Multi-unit auctionsMulti-unit auctions

Solution to lumpy bid problem: allow bidders to bid with supply schedules (use multi-unit auctions)

Example: 1) Will fence off 20 hectares at $50/ha, 50

hectares at $65/ha, etc.2) Will fence off 20 hectares at $50/ha, will fence

and enhance the native vegetation on those 20 hectares if paid $100/ha, etc.

Multi-unit auctionsMulti-unit auctions

Multi-unit auctions are widely in financial and electricity markets:

• Electricity market (UK, US, Australia)• Allocation of foreign currency• Sale of Treasury bonds

• However, the choice of payment formats is a subject of controversy

Multi-unit auctions: payment rule Multi-unit auctions: payment rule matters!matters!

Discriminatory pricingDiscriminatory pricing (pay-as-bid) (pay-as-bid):: each each winning bidder winning bidder is is paid paid based on its own based on its own bid, i.e. payment equals the cost (area bid, i.e. payment equals the cost (area under the curve) implied by the bidunder the curve) implied by the bid

Uniform pricingUniform pricing: winning bidders are paid the clearing price – : winning bidders are paid the clearing price – the marginal winner/loser sets the pricethe marginal winner/loser sets the price

Generalized Vickrey (Clinched or Ausubel auction in an open-cry format): The payment is equal to the price that would have The payment is equal to the price that would have been paid if the unit had to be sourced from the other bidders.been paid if the unit had to be sourced from the other bidders.

Payment rules: A numerical examplePayment rules: A numerical example2 bidders with 4 units to sale each. Total demand is 4 units

Bidder 1 Bidder 2

1 23 46 57 9

Uniform: Price = 4R1 = 4+4=8 R2 = 4+4=8

Discriminatory: R1 = 1+3=4 R2 = 2+4=6

Generalized Vickrey (clinched)R1 = 9+5=14 R2 = 7+6=13

Payment rules …

Residual demand facing bidder i

Supply schedule by bidder i

Payment under discriminatory

Payment under uniform

Payment under generalized Vickrey

Cut-off price

Qi(b)

Di(b) = DT - Q-i(b)

What auction design?What auction design?• Economic theory does not provide a complete picture of Economic theory does not provide a complete picture of auction perforamce ranking in the case of multi-unit auctions auction perforamce ranking in the case of multi-unit auctions (no RET): (no RET):

• Bidding truthfully under generalized Vickrey is a weakly Bidding truthfully under generalized Vickrey is a weakly dominant strategy. Supply inflation otherwise. No closed dominant strategy. Supply inflation otherwise. No closed form solution.form solution.• Controversy on the best payment scheme ( Binmore and Controversy on the best payment scheme ( Binmore and Swierzbinski 2000)Swierzbinski 2000)

• Few empirical data analyses (Wolfram, 1998)Few empirical data analyses (Wolfram, 1998)• Simplified experiments (Alemgeest et al, 1998; Kagel andSimplified experiments (Alemgeest et al, 1998; Kagel and Levine, 2001; etc.)Levine, 2001; etc.)• Need for rapid simulations: development of agent-based Need for rapid simulations: development of agent-based models (Bower and Bunn, 2001, Binmore and Swierzbinski models (Bower and Bunn, 2001, Binmore and Swierzbinski 2000)2000)

The experimental auction settingThe experimental auction setting

• We use agent-based modelling or computational We use agent-based modelling or computational experiments to explore the issueexperiments to explore the issue• Sealed-bid multi-unit procurement auction: Sealed-bid multi-unit procurement auction:

- bidders (farmers) are allowed to make multiple - bidders (farmers) are allowed to make multiple bids bids - the regulator has a target (demand level), chooses - the regulator has a target (demand level), chooses the clearing price and buys units accordingly. the clearing price and buys units accordingly. - payments depend on auction format: - payments depend on auction format: discriminatory, uniform and generalized Vickreydiscriminatory, uniform and generalized Vickrey

The agent-based modelThe agent-based model Agent-based models use computational experiments Agent-based models use computational experiments

– An artificial society of bidders (bidder agents)An artificial society of bidders (bidder agents)– Agents with cost and capacity characteristics and Agents with cost and capacity characteristics and

learning ruleslearning rules– Agents – do not get tired, bored, etc – an issue with Agents – do not get tired, bored, etc – an issue with

complex auctions if people are used (losers spoiling complex auctions if people are used (losers spoiling experiments if they are not winning)experiments if they are not winning)

Each agent i has a true cost functionEach agent i has a true cost functionPPii = a = aii + b + bii Q Q

Agents update bids through reinforcement learning. Agents update bids through reinforcement learning. After each auction, it exploits the outcomes of previous After each auction, it exploits the outcomes of previous bids or experiments with new bids: bids or experiments with new bids:

BBiiLL = a = aii L(t)L(t) + b + bi i

L(t)L(t) Q Q

Reinforcement learning algorithmReinforcement learning algorithm

(Roth & Erev GEB 1995; Erev & Roth AER 1998)(Roth & Erev GEB 1995; Erev & Roth AER 1998)– Asserts that the propensity to use an action or a strategy is Asserts that the propensity to use an action or a strategy is

positively related to the results obtained from it (positively related to the results obtained from it (exploitingexploiting known strategies)known strategies)

– And agents also And agents also experimentexperiment with strategies similar to those with strategies similar to those that they have tried and benefited fromthat they have tried and benefited from

– RecentRecent experience has more impact than past experience experience has more impact than past experience

– Learning algorithm suitable for the auction problem:Learning algorithm suitable for the auction problem:individual learning - no need to evaluate payoffs of individual learning - no need to evaluate payoffs of foregone strategies – no need to know about other bidders’ foregone strategies – no need to know about other bidders’ strategiesstrategies

Strategy (c,d)

Neighbours of (c,d)

a choice

Neighbours

Strategy

b choice

• Law of effect• Experimentation• Recency

Propensity of player i to choose strategy (a,b):

Experimental set up of simulationExperimental set up of simulation

•Simulation experiments with two populations having the same aggregate supply

- Homogeneous population: 6 bidders, ms =2 - Heterogeneous population: 2 small (S), 2 medium (M) and 2 large (L)With capacity: ms(S) = 1 ms(L) = 3 ms(M) = 2With cost structure: C(M)= 2*C(S) ; C(L) = 3*C(S)*** scale effect is removed: a medium one is exactly like 2 small ones in terms of cost structure

• Auction outcomes simulated for different degrees of rationing: from 10 to 60% of aggregate capacity

Evaluating auction performanceEvaluating auction performance

• Comparing auction outcomes:Comparing auction outcomes:• Two Two efficiency criteria:efficiency criteria:

- budgetary efficiency - outlay per unit

- allocation allocation- social cost per unit of service or good purchased through the auction

-Are you sourcing the service/good from the least cost providers?

ResultsResults

• Different patterns of bidding strategies under the three auction formats

• Vickrey leads to the highest frequency of truthful bidding (and highest proportion of Nash equilibria)

• Uniform format leads to overbidding: - with supply inflation observed at low demand levels

- a mix of high flat bidding and supply inflation at high demand levels

• Bidding under the discriminatory is the least sincere. High flat bidding is the most frequent strategy butsupply inflation observed for low levels of demand

Homogeneous population: bidding strategies

Bidding strategies: uniform auction

-0.5 0.0 0.5 1.0 1.5 2.0

0.0

0.2

0.4

0.6

0.8

quantity

au

ctio

n c

lea

rin

g p

rice

(u

nifo

rm)

D = 1.2

true curve

D = 2.4

D = 3.6D = 4.8D = 6.0

D = 7.2

Bidding strategies: discriminatory

-0.5 0.0 0.5 1.0 1.5 2.0

0.0

0.2

0.4

0.6

0.8

quantity

au

ctio

n c

lea

rin

g p

rice

(d

iscri

m.)

D = 1.2

true curve

D = 2.4

D = 3.6

D = 4.8

D = 6.0

D = 7.2

1 2 3 4 5 6 7

0.0

00

.05

0.1

00

.15

0.2

00

.25

demand

MS

D a

(le

arn

t e

ntr

y p

rice

)

VickreyDiscrim.Uniform

VickreyDiscrim.Uniform

VickreyDiscrim.Uniform

Bidding strategies: deviations in entry prices (homogeneous bidders)

Bidding strategies: deviations in bid slopes (homogeneous bidders)

1 2 3 4 5 6 7

0.0

20

.04

0.0

60

.08

demand

MS

D b

(le

arn

t su

pp

ly s

lop

e) Vickrey

Discrim.Uniform

VickreyDiscrim.Uniform

VickreyDiscrim.Uniform

• Discriminatory: strategies are not sensitive to size – big and small misrepresent true costs

• Uniform and Vickrey: coordination at high prices- large bidders adopt a “supply inflation” strategy - small bidders “free ride” on the risks taken by the bigger ones (are more truthful)

Heterogeneous population: bidding strategies

• Uniform and Vickrey auctions lead to similar results for most levels of demand.

• Uniform and Vickrey perform better than Discriminatory auction when competition is not very weak

• When competition is very weak, Vickrey rule is the worst performer

• Outlays with a heterogeneous population slightly higher than with a homogeneous population

Budgetary performance: summaryBudgetary performance: summary

Budgetary performanceBudgetary performance

1 2 3 4 5 6 7

0.1

0.2

0.3

0.4

0.5

0.6

demand

ou

tlay

pe

r u

nit

VickreyDiscrim.Uniform

VickreyDiscrim.Uniform

VickreyDiscrim.Uniform

Social cost efficiencySocial cost efficiencyMeasured by the production costs of units sold: Auctions perform equivalently for the two populations

1 2 3 4 5 6 7

0.0

50

.10

0.1

50

.20

demand

pro

du

ctio

n c

ost

pe

r u

nit

VickreyDiscrim.Uniform

VickreyDiscrim.Uniform

VickreyDiscrim.Uniform

Further research…Further research…

• Further refinements needed:• Remove assumption of linear bidding curves

• Other sources of competition• consider changes in number of bidders in addition to changes in the degree of rationing

• Computational experiments useful for completing the picture: Compared to existing theoretical results, it depicts a richer pattern of bidding strategies that depend on the interplay between heterogeneity in the bidder population and the degree of rationing (competition) in the auction

• Discriminatory the least performer except when competition is very weak

• Policy advice ?

ConclusionConclusion

• Experiment with multi-unit auctions – they can only improve auctions

• And experiment with payment formats other than discriminatory pricing

• Uniform pricing could be attractive:• simple and familiar• “equitable” • lower information demand on bidders (“you

get paid what the market offers”)• potential budgetary savings and efficiency• learning about true opportunity costs (more

truthful bidding)

Policy advice

Multi-unit Auction for Perennial Pasture

Establishment and Recovery (MAPPER)

(a multi-unit, uniform price auction)

Frank D’Emden, NRM Development Officer, DAFWA Esperance

Objectives

Strategic objective• Reduce sedimentation of Young River & Stokes Inlet

Operational objective• Establish perennial pasture filter strips adjacent to

waterways• Contain riparian saline discharge

How will it work? The EOI

=

Auction for Perennial Pastures

WHAT IS THE AUCTION FOR PERENNIAL PASTURES? The Auction for Perennial Pastures aims to develop voluntary partnerships with landholders for the establishment and rehabilitation of perennial pastures in the Young River catchment. The project, organised by the Department of Agriculture and Food WA with assistance from the Esperance Regional Forum and the University of Western Australia, is funded by the South Coast Regional Initiative Planning Team (SCRIPT) through the National Action Plan for Salinity and Water Quality and the Natural Heritage Trust. All landholders within the Young River Catchment are invited to participate in the auction. The objective is to reduce sediments flowing into the Young River and Stokes Inlet through the establishment and maintenance of perennial pastures on sloping land. A secondary aim is to control dryland salinity where it is contributing to stream bank erosion. SUBMITTING A TENDER The aim of this tender is to allow landholders to bid in flexible ways. You are encouraged to nominate an area or different areas on your farm where you could plant perennial pastures in 2007. The value of your bid should reflect the associated establishment costs. You are also allowed to nominate the prices (in dollars per hectare) that you would like to receive to proceed with each level of your nominated perennial cover. For example, you could submit

Expression of Interest Closing Date: 15/1/07

How will it work? The Bid

AREA ID* (ha) Total area (ha) Bid ($/ha) Tender amount

1 (50) 50 65 $3,250

2 (20) 70 70 $4,900

3 (20) 90 80 $7,200

* Use the same ID number on the property map

• Up to 3 ‘incremental’ bids

• $/ha may vary between increments

How will it work? The Plan

Environmental Benefit Index (under progress)

EBI = R + 2(F + S) ∑

• Reflects objectives

• Prioritises operational objectives

Where: R = ha on recharge zone

F = ha on filter/buffer

S = ha on slope >4%

∑ = total ha in bid

HydroEconHydroEcon HydroEcon has been in development for the last three years within a dryland salinity CRC project Motivation: provide a virtual laboratory for testing the economic and environmental effects of policy interventions aimed at land use practicesThe model has three layers (components) – next slide

Layers in HydroEconLayers in HydroEcon

Policy layer

Farming community layer

Agent-based implementation of whole-farm models (MIDAS-type) and auction

models

Biophysical layer

SWAT suite of hydrology, water quality, and other models

ApplicationApplication The Katanning region in WA has been selected as the area for its first application

A catchment with an area of about 300,000 haMixed crop and livestock (sheep) farmsThe farm model

eight crop, pasture and tree land uses using data from MIDAS and also from recent work by Ross Kingwell and others in relation to salinity management

Application …Application …However, the model is developed in such a way that its structure is transferable to other catchments (e.g. number and nature of crop enterprises can be varied)Although that does not mean it is ‘easy’ to set-it up (or parameterize it) for other catchments

Both MIDAS and the SWAT models require substantial amounts of data

Thank youThank you

email: email: ahailu@are.uwa.edu.auahailu@are.uwa.edu.au

Questions?Questions?Comments?Comments?